@Article{CiCP-38-711,
author = {Ehrhardt , Matthias and Zheng , Chunxiong},
title = {Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {3},
pages = {711--728},
abstract = {<p style="text-align: justify;">We propose a novel approach to simulate the solution of the time-dependent
Schrödinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Weyl $m$-function (exact Dirichlet-to-Neumann operator) by a rational
function with respect to an appropriate spectral parameter. By using this method, we
overcome the usual high-frequency restriction associated with absorbing boundary
conditions in general variable potential problems. The resulting fast computational algorithm for absorbing boundary conditions ensures accuracy over the entire frequency
range.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0178},
url = {http://global-sci.org/intro/article_detail/cicp/24313.html}
}